I find it really helpful to write down lists of things when I've got too much in my head. Then I figure out what I can do something about in the short term, because I find that doing ANYTHING, even if it's just a teensy tiny baby step, towards solving my problems feels infinitely better than doing nothing.
Here's some stuff that works for me. I hope it works for you:
What are all the things that are causing you anxiety right now? Make a list and "pick the low-hanging fruit", that is, find something that you can take care of easily, like a plan for the cats.
What's the first step in finding a new caretaker? How about posting to Craig's List? How about placing an ad in your school's newspaper? Many places have cat societies that will take your animals (and take care of them indefinitely) if you can't find an owner on your own.
Try to prioritize the things that are bothering you. Maybe you'll find that worry #10 isn't really that important.
Also, for the short term, you may want to consider medication for your anxiety if you have the means. If not, try to force yourself to do some exercise - walk at least 2 miles per day and some simple meditation to manage your stress. Find yourself a comfortable position - laying down, sitting upright, whatever, close your eyes, place your hands somewhere comfortable, and breathe deeply and slowly. When you breathe, your stomach should be doing the most moving, not your chest. Focus only on your breathing. It might help. Maybe even a lot.
Let me know if I can be of any more help and keep me posted on how it's working out for you.
Hang in there, brother. You'll pull through.